The Manuscripts file format contains inside of it a full bibliographic reference database, in a fully structured form. That your bibliography data is kept separate from the manuscript body has a number of workflow benefits over a typical word processor which relies on an external citation tool to format and contain bibliography data:

You can re-format the in-text citations and bibliography on changing the citation style.

You and your collaborators can use a mixture of reference management tools when writing the manuscript.

You can export the bibliography data out from the document into a separate BibTeX formatted file as part of the LaTeX compilation.

For power users, Manuscripts bundles in a number of command line tools from the bibutils suite to manipulate bibliography data, allowing you to for instance effectively export the bibliography from your manuscript into a number of formats beyond BibTeX (we may make a feature available in the app's UI also in future updates to accomplish the same).

To export your bibliography, follow these steps:

Export your manuscript to LaTeX (make sure you have selected either BibTeX or bibLaTeX).
2 Open /Applications/Utilities/Terminal.app, and navigate to the folder containing your exported manuscript.

To break the above command down, the bibtex file created by Manuscripts is first converted to an intermediate XML form (the MODS format, using the bib2xml command), and then converted from that to the EndNote ENW format. On top of xml2end which converts to ENW, there are also tools included for converting to a number of other reference file formats: